Animation by adding points to a curve, with Python?
I had this exact same problem a couple of months ago.  The solution irc provided to me was to create a full curve and animate the End Bevel Factor.


The beginning of your curve is bevel_factor=0.  The end of your curve is 1.0.  I am pretty sure it maps from the bevel factor to the index of a control point. So if your curve has 11 points (0..10), then bevel 0.3 will include control points (0..3) .

Consider carefully if you want to animate it with a linear animation curve or the default bezier curve.